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XAT 2012 — QA & DI Question 19

BasicsEasy
Passage / Data

Answer the following question based on the information given below.

Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.

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Shyam, a fertilizer salesman, sells directly to farmers. He visits two villages A and B. Shyam starts from A, and travels 50 meters to the East, then 50 meters North-East at exactly 45° to his earlier direction, and then another 50 meters East to reach village B. If the shortest distance between villages A and B is in the form of ab+c meters, find the value of a + b + c.

Answer & solution

  • A

    52

  • B

    54

  • C

    58

  • D

    59

  • None of the above

Solution

Total distance travelled by Shyam is;

50+50+502 km towards east, and 502 km towards north

Hence, smallest distance, say d, between village A and Village B is;

d=((100+252)2+(252)2)

Hence, d2=(100+252)2+(252)2=a2(b+c)

But, (100+252)2+(252)2=2500(5+22)

=2500(5+8)

Hence, a2 = 2500, b = 5 and c = 8

Hence, a + b + c = 50 + 5 + 8 = 63

Hence, option (e).

XAT 2012 QA & DI Q19: Shyam, a fertilizer salesman, sells directly to farmers. He visits two villages A and B. Shyam starts from A, — Solution | TheCATExam